Embodiments of the present invention relate to the measurement of polarization mode dispersion (PMD) in fiber optics, and more particularly, to systems and methods for measuring PMD by observation of data-bearing signals.
The transmission of information on beams of light sent through optical fibers is a large and active industry. The information, in the form of logical 0's and 1's, is modulated onto the light beam. For many years, the mode of modulation was to switch the light on and off. Recently, advanced modulation formats have been deployed, which allow more than one bit of information to be encoded on each modulated symbol. The phase and the state of polarization (SOP) of the light may be modulated in these advanced modulation formats. Polarization multiplexing may be employed, where two signals are combined on orthogonal SOPs so as to double the information carried. For example, the dual polarization quadrature phase shift keying format (DP-QPSK) is one such conventional method. While direct detection was sufficient for on-off modulated signals, a more complex type of detection called coherent detection is typically required to receive the advanced modulation formats. The difference between direct detection and coherent detection is known among people with skill in the art and is explained in the book “Fiber-Optic Communication Systems” by G. P. Agrawal (Wiley, 2nd Ed., 1997).
Another technology that has been applied in fiber optic receivers recently is digital signal processing (DSP). Previously the processing executed in a fiber optic receiver was quite simple. An electrical circuit made a decision whether the optical power was above or below a certain threshold, to declare whether a symbol was a logical 1 or logical 0. With DSP, electrical signals within the receiver are digitized, that is, converted into a sequence of numerical values, which are then acted on by a series of arithmetic operations to eventually compute the information content of the signal. Digital signal processing performs the extra operations needed for coherent detection, compared to direct detection. The DSP receiver has an additional advantage. The optical signal may be distorted by propagation through the optical fiber, and digital signal processing operations may be applied within the receiver to correct for the fiber propagation impairments. Some of these impairments, such as PMD, vary over time. The DSP is able to track the variation, and continue to correct for the impairment as it varies. While there are adaptive equalization algorithms that correct for an impaired signal without knowing the nature of the impairment, it is often more efficient to apply an algorithm that first estimates the amount of impairment and then corrects for it.
The optical signal may propagate over a large distance of optical fiber, hundreds or thousands of kilometers, before it is detected and the information content extracted. The signal decays due to fiber attenuation, but it may pass though many optical amplifiers, each one boosting the signal to a high power. The optical amplifiers do not correct for any impairments, so propagation impairments accumulate over the full distance between transmitter and receiver.
Fiber optic communication systems typically employ wavelength division multiplexing (WDM), which means that several optical signals are sent over the fiber in parallel, at different wavelengths. The WDM channels are grouped in bands, depending on what kind of optical amplifier is used. The most common band to be used is the C-band, which is 35 nanometers (nm) wide centered on 1550 nm. Each WDM channel occupies a small range of wavelengths. For example, a 28Gbaud DP-QPSK signal typically occupies 19 gigahertz (GHz) of optical spectrum, which is equal to 150 picometers (pm) in wavelength terms in the C-band.
Polarization mode dispersion is one of the most important fiber propagation impairments. When a fiber has PMD, it means that light in one state of polarization travels faster than light in the other (i.e., the orthogonal) SOP. Typically, a signal may lie in a mix of both the fast and slow SOPs, and at the receiver, the signal is distorted because light from one symbol arrives on top of light from a preceding symbol. This is referred to as inter-symbol interference. The root cause of PMD is that the fiber has birefringence because it is not perfectly circular, or because it is under strain due to a bend in the fiber. Birefringence means that the refractive index (which controls the speed of light) is different between two orthogonal states of polarization. A complicating feature is that the axes of birefringence, the fast and slow polarization states, typically do not align over the length of the fiber, but are randomly oriented from one section of fiber to the next. Also, the alignment between sections effectively changes over time as the stress on the fiber changes due to temperature, or if a fiber cable is moved. This means that the effect of PMD on the signal is different for different WDM channels, and the effect on any one WDM channel varies over time, perhaps as quickly as a few milliseconds.
In general, there are two ways to characterize the polarization mode dispersion of a long length of fiber. Both measured quantities are sometimes called “PMD,” although there is an important difference between the two measured quantities. In one mode, the average PMD is measured by sending a broadband light source, whose spectrum is many nanometers wide, through the fiber. The average PMD is reported as a single value in time units (e.g., a number of picoseconds), which represents the average (root mean square) amount of time delay between the fast and slow SOPs. The average can be expressed over time and wavelength. Alternatively, the instantaneous PMD, seen by one WDM channel at one time, may be measured. It is the instantaneous PMD that is of interest if one wants to compensate for the PMD seen by an optical signal, and there is no benefit in this situation in knowing the average PMD of the fiber. As used herein, any further mention of “PMD” refers to the instantaneous PMD.
The PMD is expressed as a set of coefficients, where each coefficient is a three dimensional vector quantity. The first coefficient is called the first order PMD, and is also known as the differential group delay. Often only the first order PMD needs to be known to fully describe how PMD affects a WDM channel. A more complete explanation of the first order PMD is given in “Measurement of polarization-mode dispersion in single-mode fibers with random mode coupling” by C. D. Poole (Opt. Lett., vol. 14, pp. 523-525, 1989). When the PMD is large enough that it varies across the bandwidth of a WDM channel, it is necessary to include the second order and higher PMD coefficients to describe it fully. A more complete explanation of the higher order coefficients is provided in “Statistical Theory of Polarization Dispersion in Single Mode Fibers” by G. J. Foschini and C. D. Poole (IEEE J. Lightwave Technol., vol. 9, p. 1439-1456, 1991). The second order PMD is the derivative, that is, the rate of change with optical frequency, of the first order PMD. The third order PMD is the derivative of the second order PMD, and so on.
One way to measure the PMD coefficients of a fiber span is the Jones matrix eigenanalysis (JME) method, described in “Automated Measurement of Polarization Mode Dispersion Using Jones Matrix Eigenanalysis” by B. L. Heffner (IEEE Phot. Tech. Lett., vol. 4, p. 1066-1069, 1992) and “Accurate, Automated Measurement of Differential Group Delay Dispersion and Principal State Variation Using Jones Matrix Eigenanalysis” by B. L. Heffner (IEEE Phot. Tech. Lett., vol. 5, p. 814-817, 1993). The JME method is based on the property of PMD that it causes the state of polarization to change as the wavelength is changed. A tunable laser is sent through the optical fiber in the wavelength region of interest, and the output SOP is observed on a polarimeter, an instrument that measures state of polarization, as the laser is tuned in wavelength. A disadvantage of this method is that it cannot be used to measure the PMD of an in-service WDM channel. The signal would have to be switched off to allow light from the tunable laser to pass through the fiber and be received by the polarimeter.
There are measurement methods that act on an information-bearing signal directly, and can be applied to in-service signals. When the signal is polarized, then PMD has the effect of partially depolarizing the signal. The degree of depolarization can be used to estimate the PMD, as described in “Method for PMD Vector Monitoring in Picosecond Pulse Transmission Systems” by L. Moller and L. Buhl (IEEE J. Lightwave Technol., vol. 19, p. 1125-1129, 2001) and “PMD monitoring in traffic-carrying optical systems and its statistical analysis” by J. Jiang et al. (Optics Express, vol. 16, p. 14057-14063, 2008). This method only works on single polarization signals, and does not work on polarization multiplexed signals.
Another method described in “Channel Parameter Estimation for Polarization Diverse Coherent Receivers” by J. C. Geyer et al. (IEEE Phot. Tech. Lett., vol. 20, p. 776-778, 2008) does work with polarization multiplexed signals. The signal at the output of the optical fiber is detected by a coherent receiver and digitized. An adaptive equalization process is applied to the digitized representation to try to improve the signal. Then the PMD is calculated from the converged coefficients of the adaptive equalizer, based on the assumption that PMD has caused the impairment to the signal. This method may be inaccurate if the signal is impaired by a different mechanism from PMD. For example, a realistic optical transmitter might have the signal on one polarization delayed by 5 ps compared to the signal on the other polarization. The adaptive equalization algorithm would conclude incorrectly that the signal has been impaired by 5 ps of first order PMD, when in fact the impairment appears at the output of the transmitter.
Accordingly, a need remains for a method to estimate the PMD associated with an optical signal by observing the signal itself. There is a need for the PMD estimation method to work with polarization multiplexed signals, and for the method to be accurate even if the signal is impaired by a different mechanism in addition to PMD. Finally, there is a need for a PMD measurement that works when the state of polarization of the signal is varying at the speeds sometimes seen in fiber optic links. Embodiments of the invention address these and other limitations in the prior art.
The foregoing and other features and advantages of the inventive concepts will become more readily apparent from the following detailed description of the example embodiments, which proceeds with reference to the accompanying drawings.